|By Greg Roumeliotis and Arno Schuetze

|By Greg Roumeliotis and Arno Schuetze

|By Greg Roumeliotis and Arno Schuetze

(Reuters) - T-Mobile US Inc <TMUS.O> is close to agreeing tentative terms on a deal to merge with Sprint Corp <S.N>, people familiar with the matter said on Friday, a major breakthrough in efforts to merge the third and fourth largest U.S. wireless carriers.

The transaction would significantly consolidate the U.S. telecommunications market and represent the first transformative U.S. merger with significant antitrust risk to be agreed since the inauguration of U.S. President Donald Trump in January.

The progress toward a deal also indicates that T-Mobile and Sprint believe that the U.S. antitrust enforcement environment has become more favorable since the companies abandoned their previous effort to combine in 2014 amid regulatory concerns.

The latest development in the talks between T-Mobile and Sprint comes as the telecommunications sector seeks ways to tackle investments in 5G technology that will greatly enhance wireless data transfer speeds.

Japan's SoftBank Group Corp <9984.T>, which controls Sprint, and other Sprint shareholders will own 40 to 50 percent of the combined company, while T-Mobile majority owner Deutsche Telekom <DTEGn.DE> and the rest of T-Mobile shareholders will own the majority, the sources said.

SoftBank founder Masayoshi Son met with Trump late last year and said in February that the Japanese firm should benefit from Trump's promised deregulation.

Once terms are finalized, due diligence by the two companies will follow and a deal is expected by the end of October, though talks may still fall through, the sources said.

A merger would create a business with more than 130 million subscribers, just behind Verizon Communications Inc <VZ.N> and AT&T Inc <T.N>. Revenues would top $70 billion and analysts say there would be massive scope to cut costs.

Sprint shares were up 5 percent in afternoon trading in New York on Friday to $8.44, giving the company a market capitalization of close to $34 billion. T-Mobile shares were up 0.4 percent to $63.66, giving that company a market capitalization of around $53 billion.

The sources asked not to be identified because the negotiations are confidential. Sprint and Deutsche Telekom declined to comment. T-Mobile and SoftBank did not immediately respond to requests for comment.

SoftBank's Son abandoned an earlier attempt to acquire T-Mobile for Sprint in 2014. Under that deal, SoftBank would have been in control of the merged company, with Deutsche Telekom becoming a minority shareholder.

Since then, T-Mobile has outperformed Sprint under Chief Executive John Legere, who the sources said would lead the combined company.

SON IN TRUMP TOWER

Earlier this month, Federal Communications Commission Chairman Ajit Pai gave a potential boost to a tie-up when he recommended that the FCC find for the first since 2009 that there is “effective competition in the marketplace for mobile wireless services.”

The FCC is set to vote on Tuesday on the proposed annual report on the state of the wireless competition market required by U.S. Congress.

T-Mobile and Sprint will likely tout planned investments in 5G and their network that would create jobs, though combining operations would also lead to layoffs, said Roger Entner, an analyst at Recon Analytics.

"They will argue that the track record of T-Mobile and Sprint shows they are vigorous competitors and that this will not cease to be the case after the deal," said Entner.

Son made headlines in early December when he appeared in the marble lobby of Trump Tower in New York alongside the president-elect, dressed in a red vest and red tie nearly identical to that of the tycoon turned commander in chief.

He was among the first in a series of Asian billionaires and leaders to pay a congratulatory visit to Trump, who won office in November on a platform that focused on national security and protecting U.S. jobs.

Son's pledge to Trump to invest $50 billion in the United States and create 50,000 jobs was light on details but spoke to the president’s election promise to boost economic growth by making deals with individual companies, rather than through complicated trade deals.

Last month, Sprint CEO Marcelo Claure said an announcement on merger talks should come in the “near future.”

Sprint had approached cable company Charter Communications Inc <CHTR.O> about a potential merger earlier this year, but quickly abandoned that effort.

AT&T is in the process of getting its own transformative deal, its $85.4 billion acquisition of media conglomerate Time Warner Inc <TWX.N> approved by U.S. regulators.

(Reporting by Greg Roumeliotis in New York and Arno Schuetze in Frankfurt; Additional reporting by Pamela Barbaglia in London, Douglas Busvine in Frankfurt, David Shepardson in Washington; Writing by Douglas Busvine; Editing by Bernadette Baum and Meredith Mazzilli)